Nonlinear analysis of the solar updraft tower under static wind action

Abstract

The near future is challenging: depletion of non-renewable energy depletion, electricity shortage and sustainability give the need of developing renewable energy technology. The solar updraft tower power generation technology using solar and wind generates a reasonable amount of electricity with zero carbon footprint during operation. The working principle is rather simple: the heated air underneath a large transparent roof (air collector) is sucked into a central vertical chimney; the driven wind generates electricity by wind turbines. The solar updraft towers are mainly suitable for high power output, which also requires a large scale structure. The solar updraft tower in this research project is a 1000m reinforced concrete tall tower stiffened by ten stiffening rings every 100m. The wind load is the most hazardous action for ultra-high ultra-thin SUT shells. The constitutive behavior of the reinforced concrete structure will give nonlinear responses under a certain wind loading level, which requires a careful study. Additionally, the SUT structural design under large wind load treated in a linear elastic stage could be costly. The dimensions of the reinforcement calculated by linear-elastic analysis can be improved by nonlinear analysis. It gives a real structural behavior including the stress redistribution caused by concrete cracking, crushing and reinforcement yielding. Nonlinear analysis can achieve a more economic design while maintaining sufficient safety. This main thesis objective is to perform a physical nonlinear analysis of the SUT under static wind action to acquire realistic structural behavior and conduct a further optimization. A finite element model is built and a linear analysis is done for the model verification. Then a detailed linear model is built to determine the necessity of detailing the stiffening rings. The analysis shows that by detailed modeling the stiffening rings provide a higher stiffness compared to modeling the simplified way, hence improving the overall structural behavior of the Solar Updraft Tower. A discussion about the feasibility of the chosen nonlinear material models has been done. The total strain crack rotating model is chosen whose crack is rotating continuously with the direction of principal stress. The simple working principle gives the model a robust and stable behavior. For concrete tensile behavior, a linear ultimate strain based stress-strain relation is used including the tension stiffening effect. A nonlinear stress-strain behavior is adopted for concrete in compression, considering effects of lateral crack and lateral confinement. For the reinforcement steel, elastoplastic material modeling is used with strain hardening. Few models according to the original design of Krätzig & Partner have been built. The shell walls have a one layer reinforcement grid located at the mid-surface of the shell walls with minimum reinforcement ratio both in the meridional and the circumferential directions. The difference between these models is the way of modeling the stiffening rings: one is modeled by 3D beam elements with 1% reinforcement ratio modeled in the longitudinal direction, and the other is modeled by curved shell elements with 1% reinforcement ratio modeled both in the longitudinal direction and the transverse direction. Both models experienced a large ovalization failure mechanism at the upper cone at the serviceability limit state. This is caused by 1) the low reinforcement ratio which provides a low stiffness to the stiffening rings; 2) The eccentricity of the stiffening rings which generates a large bending moment, thus weakening the ring-wall connections. The model with beam elements showed weaker structural response than the model with curved shell elements because the beam elements do not take the transverse stiffness into consideration. The model using curved shell elements is adopted for further nonlinear analysis. Models with increasing reinforcement ratio in two directions up to 3% on the stiffening rings are built to improve the structural behavior. The stiffness of the Solar Updraft Tower has improved, which gives less ovalization deformation. However, all models experienced the ovalization failure mechanism at a certain loading stage. Unfortunately, the concrete crushing and reinforcement yielding still occur, even with the maximum reinforcement ratio on the stiffening rings. It is because the large bending crack at the ring-wall connection caused by the eccentricity of the stiffening rings decreases the contribution of the stiffening ring to the overall structural behavior. Several models are built using the same reinforcement ratio in two directions on the stiffening rings with increasing tension stiffening effect. The nonlinear result shows that the influence of tension stiffening rings is high at a low loading level and is decreasing at a higher loading level. One possibility of removing the bending failure at the ring-wall connection is to move the mass center of the cross-section of the stiffening rings to the mid-surface of the shell walls. Two re-centered models with increasing reinforcement ratio are built. With 1% reinforcement ratio, the model with re-centered stiffening ring gives a similar structural response as the original design model with a reinforcement ratio of 2%. The re-centered model with 2% reinforcement ratio gives an almost linear behavior of the structure without ovalization failure mechanism at the upper cone. No cracking is found both at the ring-wall connection and the concrete shell wall, no concrete crushing occurs and also no reinforcement is yielding. A maximum deflection around 1m meets the requirement of the maximum allowable displacement in the serviceability limit state. However, a large crack width of 1.1mm is found in the stiffening rings which should be further improved by modeling the structure using two layer reinforcement or by prestressing. Last but not least, the effect of moving the stiffening rings inside the airflow on the power output should be further investigated. But re-centering geometry gives a triple time of improvement on the structural behavior, and eventually saved a high amount of material use.